To clarify: “Lightroom” (often abbreviated to ”Lr”) IS the cloud centric option. This gives you the option of working in a mobile device, or in the web browser, or in a desktop installed application. This last is usually called the “Lightroom desktop app” because it is a desktop interface for accessing your “Lightroom” image library, which as above: lives in the cloud and stores its files there.
The product called “Lightroom Classic” (abbreviated often to LrC) employs a locally stored Catalog instead. It can optionally sync albums of images into the cloud or not, but its file storage and all of its functions operate completely within your local computer.
As has been explained, there are two ways to start LrC. If you have an active Creative Cloud plan you can open it from there. But also, this is a standard installed application and you can use your Windows or Mac normal means of opening this. Provided it has not been uninstalled.
Also: provided you have in fact been using Lightroom Classic up to now - and not (you would not be the first person!) installed and used the Lightroom.Desktop App under the mistaken impression that this was Lightroom Classic.
In the case of Windows, assuming LrC, you can look in your Start menu - you may need to open all apps. Once you have found it, you can right-click and choose Pin to Taskbar or else Pin to Start. Sometimes you may need to go into ‘show more options’ in the right-click menu to see these options. That will create a clickable icon for starting LrC. MacOS will I expect be equivalent but different - someone else would have to advise on that.